Homework 4-

Question 1- The economy of country A is described by the production function: Y = √KL.

In this equation the symbol Y stands for real GDP, K for capital and L for the employed individuals in this economy. The labor force at the beginning of time, period 0, is 100 individuals. Capital in each period is constant and equal to 120 units. Every period the labor force increases by 100 individuals and the unemployment rate stays constant at 10% of the labor force. (Suggestion: Use Microsoft Excel or some other computer program to do the calculations and the graphs of the questions posed below rather than a regular calculator. On the homework page of the class website is a link to some helpful guidelines for using Excel.)

a. Complete the following chart using the above information. Calculate real GDP with at least 3 decimal places. Hint: this will be far easier if you use Excel to do these calculations and you may present your own Excel Chart as the answer to this question.

b. Graph Real GDP and the employment level for this economy. Please measure real GDP on the y-axis and employment on the x-axis. For this question it is fine to present your answer as an Excel Graph (hint: this is much easier to do with a program like Excel).

c. Suppose now that instead of capital being constant at 120 units during the periods of our analysis capital is instead equal to 240 units. Nothing else changes about this problem (e.g., the labor force still increases as described earlier in the problem). In one graph present real GDP under both situations: situation one, where capital is equal to 120 units and situation two, where capital is equal to 240 units. On your graph measure real GDP on the y-axis and employment on the x-axis. (Hint: once again, this will be easier to do if you use Excel to calculate the necessary values and then use Excel to graph the two situations.)

d. Suppose the level of employment is equal to 180 people. What is the percentage change in the productivity of labor from the first situation when capital is equal to 120 units to the second situation when capital is equal to 240 units? 

e. Using the previous information assume that for period 0 we know that this economy consists of two types of firms, agricultural and industrial firms.

Agricultural firms have a labor demand given by:

W/P = 4000-(L_agriculture/3)

Industrial firms have a labor demand given by:

L_industry = 3000-(W/P)*(7/8)

where W/P is the real wage rate and L refers to labor demand (thus L_agriculture is the demand for workers by the agricultural firms). Assume that in period 0 the aggregate price level P is equal to 1, and therefore the real wage (W/P) is equal to the nominal wage (W). Find the aggregate labor demand in this economy and then calculate the real wage in this economy for period 0.

Question 2- Each of the following questions involves calculating some aspect of real GDP.

a. A day before his birthday (June 6, 2009) Bruno sells his hair salon for $100,000. In addition he sells his car (produced in 2002) for $25,000. That same day he provides 5 hair cuts for $15 per haircut. On his birthday he dies leaving an inheritance of $125,000 to his best friend.

The change in GDP due to these events is _____________

b. Bakery A annually uses $10 million worth of sugar, flour, and eggs (assume all three of these ingredients are produced in the same year that the bread is produced) to produce its bread. Wages and salaries in Bakery A for the year are equal to $40 million; the bakery's only other annual expense is $15 million in interest that it pays on its bonds. The annual profits for the owner of the bakery are $ 10 million.

The bakery's annual effect on GDP equals ______________

c. On April 30, Carlos decides to stop throwing away $60 a month on convenience store ice cream.  In the economy where Carlos lives, supply=demand at every moment in time: thus, Carlos' decisions immediately affect firm output. At the same time that Carlos stops buying convenience store ice cream, he buys $200 worth of equipment, milk, butter, sugar, and cream and makes his own ice cream for the rest of the year.

The change in GDP due to these actions by Carlos is ______________

d. Laura, who lives in Nebraska, finds $50,000 in a garbage bag this year when she goes to throw away her own garbage. Instead of reporting it to the authorities she decides to start her own business. To do so she buys $32,000 worth of equipment from Torcidos Ltd. of Venezuela and $18,000 from Tornado Ltd. from Washington, Kansas. Both purchases are made during this year and all the equipment was produced during this year.

The change in GDP due to Laura's actions is equal to ______________

e. Econ Artists, Inc., located in Newton, Massachusetts produces 100,000 new Macroeconomic books this year and it prices each textbook at $115. These textbooks are basically the same book as last year's textbook with the addition of some new graphs and examples. 10,000 of these textbooks are sold abroad and 60,000 of these textbooks are sold in the US. The remainder of the textbooks produced this year remain unsold on warehouse shelves.

The contribution to this year's GDP from Econ Artists, Inc. is equal to ______________

List of Notations for Next Two Questions

C = Consumption            

S_Private = Private Saving

I = Investment 

S_Government = Government Saving

G = Government spending         

T = Tax

X = Export          

TR = Government Transfers

IM = Import       

KI = Capital Inflow

Question 3- Classical Model.

By definition, we have the following equations:

Expenditure = C + I + G + X - IM,                         (1)

Income = C + S_private + T - TR                             (2)

S_Government  = T - TR - G                                    (3)

and

KI = IM - X                                                          (4)

In a loanable funds market equilibrium, we have

I = S_Private+ S_Government  + KI                           (5)

a) Show that, in a loanable funds market equilibrium, we have

I = S_Private - G + T -TR - X + IM

b) Show that if the loanable funds market is in equilibrium, we must have

 Expenditure = Income

c) Explain why capital inflow is equal to IM - X instead of X - IM.

Question 4- Fiscal Policy.

We know that, in a loanable funds market equilibrium, we have

I = S_Private + S_Government  + kKI

which implies that

I = SPrivate - G + T - TR - X + IM

a) Suppose the government of an economy decides to increase its spending. Holding everything else constant, what are the effects of the increase in government spending on the loanable funds interest rate and the equilibrium level of investment?

b) Suppose the equilibrium level of investment is exactly equal to the depreciation of the economy's capital for the year. That is, the quantity of capital is constant over time. Suppose the government increases its level of spending holding everything else constant and that furthermore, this increase in government spending has no effect on the equilibrium level of employment. What is the effect of this increase in government spending on output and output per unit of labor?